CN112665509B - White light interferometry method for self-correcting scanning error - Google Patents
White light interferometry method for self-correcting scanning error Download PDFInfo
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Abstract
The invention provides a white light interferometry method for self-correcting scanning errors, which comprises the following steps: collecting an interferogram using a white light interferometry device; calculating the definition of the interference pattern by using a definition operator, and marking an effective interference pattern; renumbering the effective interferograms and dividing into P groups; calculating the gray level change of pixel points on each group of effective interference patterns along the sequence number direction, and marking the pixel points as effective pixel points; calculating a phase shift stepping value by adopting a phase shift calculation method; calculating the scanning height according to the phase shift stepping value; then calculating the modulation degree and the phase of each pixel point on each group of characteristic interferograms; and finally, calculating the height of the pixel point. By adopting the scheme, the actual scanning step length in the white light interferometry can be calculated at high precision, the measurement error caused by the scanning step length is effectively compensated, and quite high precision is obtained.
Description
Technical Field
The invention relates to the field of optical measurement, in particular to a white light interferometry method for self-correcting scanning errors.
Background
The white light interference technology is an important technology for measuring the microscopic surface, the precision can reach the nanometer level, and the white light interference technology is widely applied to the fields of machinery, microelectronics, material biology and the like. The white light interference scans the surface of the sample vertically in the working process to obtain coherent interference signals of each point on the surface. When the optical paths of the sample surface and the reference mirror are equal, the contrast of the coherent interference signal is maximum. Therefore, by analyzing the coherent interference signal at each point, the height information at that point on the sample can be determined. The accuracy of the scanning step length is directly related to the precision of white light interferometry, and is the most concerned parameter of white light interferometry. However, due to the errors of linearity and nonlinearity of the scanner itself and the influence of environmental vibration during the use, the scanning step length of the measurement process deviates from the preset value, and finally the measured surface has significant errors. Scanning errors mainly affect two links of white light interferometry: 1. leading to modulation degree and phase calculation errors, and influencing coherent envelope peak position extraction and phase restoration; 2. the step length is deviated from the preset value, and an error is directly generated when the surface height is reconstructed.
In order to solve the problem of scanning errors in white light interferometry, researchers have developed two methods, active and passive, both of which utilize a fixed relationship between the scanning step and the phase. The basic idea of the active method is as follows: additional interferometric light paths are used to quickly detect the phase change between the reference mirror and the surface being measured, and to calculate the scanning error, and then drive the scanner to compensate for the scanning error (A. Olszak et al, High-stability white-light interference with reference signal for real-time correction of scanning errors, Opti. Eng., 2003; L. Ch. Chen et al, In-situ scanning white light interference with scanning accuracy and active sampling, In. J. Nanomanning measuring, 2012012; S. Terrestrik et al, vision compensated scanning light interference-light-interference-spectrum-spread, SPIE, 7). The active method can compensate the scanning error in real time, but the optical path is relatively complex, and the requirements on the control speed and precision are relatively high. The basic idea of the passive method is as follows: analyzing the collected interference signals, analyzing the phase shift change between interferograms by a calculation method, calculating the change of the optical path difference by using the relation between the phase and the optical path difference, further obtaining the actual scanning step length, and compensating the scanning error when reconstructing the surface height (J.Schmit, etc., High-precision shape measurement by white-light interference with real-time scanner error correction, application.Opti.2002; J.Wiersma, etc., vision sensitive extended range interference optics, application.Opti.2013). The passive method does not add any change to the white light interference measuring device, so the structure is simple and the cost is low. However, the current passive method has a high requirement on the uniformity of the actual scanning step, so the calculated scanning step is only suitable for the low-frequency vibration interference, and is not suitable for the medium-high frequency or random scanning error.
The problem of scanning errors in white light interferometry has not been effectively solved in the industry. Therefore, the method for accurately calculating and compensating the scanning error has important significance for popularizing the white light interferometry technology, improving the measurement precision and expanding the application occasions.
Disclosure of Invention
The invention provides a white light interferometry method with scanning error self-correction for solving the problems, by adopting the scheme, the actual scanning step length in the white light interferometry can be calculated with high precision, the measurement error caused by the scanning step length is effectively compensated, and quite high precision is obtained.
The technical scheme adopted by the invention is as follows: a white light interferometry method for self-correcting scanning errors comprises the following steps:
s1: collecting N interferograms along the vertical direction by using a white light interferometry device; wherein λ is the equivalent wavelength of the white light interferometry device, σ is the angle wave number corresponding to the equivalent wavelength λ, and σ is 2 pi/λ;
s2: respectively calculating the definition of the N interference patterns by using a definition operator, and marking the effective interference patterns according to the definition;
s3: arranging the obtained effective interferograms into an effective interferogram sequence according to the sequence of the collected sequence numbers from small to large, coding again, and continuously sequencing the effective interferogram sequence according to the sequence numbers to divide the effective interferogram sequence into P groups, wherein each group has Q interferograms;
s4: calculating the gray scale change of pixel points on each group of effective interference patterns along the sequence number direction, and marking effective pixel points;
s5: calculating phase shift stepping values of all effective pixel points on each group of effective interferograms by adopting a phase shift calculation method;
s6: calculating the scanning height of each interferogram in the effective interferogram sequence relative to the first interferogram according to the phase shift stepping value;
s7: dividing the effective interferograms into G groups, wherein each group has T interferograms, defining the T-th interferogram in each group as a characteristic interferogram of the group, and calculating the modulation degree and the phase of each pixel point on each characteristic interferogram;
s8: and searching the serial number with the maximum modulation degree value in the serial number direction, and calculating the height of the pixel point according to the modulation degree and the phase.
Further preferably, the step S2 further includes the following sub-steps: calculating the resolution as Si(i-1, 2, …, N) or Si>And ths, recording the interference icon of the ith frame as an effective interference map, wherein the ths is a preset threshold value.
Further preferably, the step S3 further includes the following sub-steps: when renumbering, the effective interference pattern is marked as Ii(x, y), where the index i is 1,2, …, M is the number of effective interferograms, and (x, y) is the number of pixel points on an effective interferogram.
Further preferably, the step S4 further includes the following sub-steps: calculating the gray scale change v of the pixel point (x, y) on the effective interference image in each group along the sequence number directionp(x,y)，vp(x,y)>thv, marking the pixel points as effective pixel points of the p-th group of effective interferograms to obtain all effective pixel points of the p-th group of effective interferograms, wherein thv is a preset threshold value;
further preferably, the step S5 further includes the following sub-steps: the calculated phase shift step value of the p-th group of the q-th interferograms is recorded as dp,qWherein P is 1,2, …, P, Q is 2,3, …, Q; averaging the phase shift step values of the R effective interferograms overlapped in the adjacent groups, directly taking the phase shift step value obtained in the step S5 from the non-overlapped effective interferograms to obtain the phase shift step value of each interferogram in the effective interferogram sequence, and recording the phase shift step value as DjJ is 2,3, …, M is the number of effective interferograms, and let D be1Where R is the number of overlapping amplitudes in two adjacent groups, 0<R<Q。
Further preferably, the step S6 further includes the following sub-steps: let the scan height be zjWhere j is 1,2, …, M, j is the interferogram number of the scan height to be calculated, DiIs the phase shift step value of the ith interferogram, sigma is the angle wave number corresponding to the equivalent wavelength lambda, and sigma is 2 pi/lambda;
further preferably, the step S7 further includes the following sub-steps: dividing the effective interferograms into G groups, wherein each group has T interferograms, two adjacent groups have T-1 interferograms which are overlapped, G is M- (T-1), the T-th interferogram in each group is defined as a characteristic interferogram of the group, and T is more than or equal to 1 and less than or equal to T; then, the modulation degree M of each pixel point (x, y) on the g group characteristic interference pattern is calculatedg(x, y) and phase
sk＝sin[2σ(zg+k-1-zg+t-1)]；
ck＝cos[2σ(zg+k-1-zg+t-1)]；
Until G groups of interferograms complete calculation, and for each pixel point (x, y), obtaining R- (T-1) Mg(x, y) and R- (T-1)
Where A is the background intensity, b is the modulation cosine component, c is the modulation sine component, SkIs the sine value of the phase shift of the g + k-1 th interferogram relative to the g + t-1 th interferogram, CkIs the cosine of the phase shift of the g + k-1 th interferogram relative to the g + t-1 th interferogram, σ is the angular wave number corresponding to the equivalent wavelength λ, and σ is 2 π/λ.
Further preferably, the step S8 further includes the following sub-steps: for pixel point (x, y), searching in the sequence number directionFind MgThe number S (x, y) with the largest numerical value (x, y); calculating the height h (x, y) of the pixel point (x, y):
wherein ZS(x，y)Is the scanning height corresponding to the pixel (x, y) on the interference pattern with the sequence number S (x, y),
the phase corresponding to the pixel (x, y) on the S (x, y) interferogram, σ is the angular wave number corresponding to the equivalent wavelength λ, and σ is 2 pi/λ.
Further optimization, the phase shift calculation method adopts three arcsine algorithms, and the three arcsine algorithms comprise the following steps:
s21: averaging the gray levels of each pixel point (x, y) of the effective interference image along the sequence number direction to obtain a background A (x, y) of the effective interference image;
s22: subtracting A (x, y) from each effective interferogram to obtain a background-free interferogram Iq'(x,y)，q＝1,2,…,Q；
S23: the phase shift step value of the q-th effective interferogram is
Q2, 3, …, Q, Pos is Iq'(x,y)>0, Neg is Iq'(x,y)<0, wherein the nominal scanning step length of the three arcsine algorithms is lambda/8.
Further optimizing, the phase shift calculation method adopts an iterative algorithm, the iterative algorithm comprises N loops, and each loop comprises a calculation part I and a calculation part II;
in said calculation part I, the time phase delta of the effective interferogram is knownqQ is 1,2, …, Q is the number of interferograms involved in the calculation of the spatial phase of the active pixel
The calculation method is
A is the background intensity, b is the modulation degree cosine component, c is the modulation degree sine component;
for cycle 1, δqIs the initial value of the input, δ for the non-1 st cycleqObtained from the calculation part II of the previous cycle;
the computing part II knows the space phase of the effective pixel point
Calculating the time phase delta of the effective interferogram of all Q interferogramsqQ is 1,2, …, Q, and the calculation method is
PixNam is the number of effective pixel points participating in calculation, A ' is the background intensity, b ' is the modulation degree cosine component, and c ' is the modulation degree sine component;
spatial phase
Obtained from the calculation part I of the cycle;
the number N of the cycles is directly specified in advance, or delta calculated by comparing two adjacent cyclesqDeviation is determined if the deviation is less thanA pre-specified threshold, the loop terminates;
phase shift step value dq＝δq-δq-1，q＝2,3,…,Q。
The working principle of the scheme is as follows: a white light interference measurement method for scanning error self-correction is characterized in that a white light interference measurement device is used for collecting N interference patterns in the vertical direction, the interference patterns are grouped, effective interference fringe areas of each group of interference patterns are judged, three arcsine algorithms or iterative algorithms are adopted, the phase shift amount of each group of interference patterns is calculated for the effective interference fringe areas, and then the actual scanning step length between the interference patterns is obtained. And after the actual scanning step length is accumulated and calculated, obtaining the actual corresponding scanning height of each interference pattern. After the actual scanning height is obtained, the modulation degree and the phase are calculated from a plurality of adjacent interferograms by a least square method. And determining the height of the measured surface by combining the actual scanning height from the calculated modulation degree and phase. The invention utilizes the characteristic of continuous movement of interference fringes in the scanning process to calculate the actual scanning step length from the interference fringes, can correct the interference of the external environment on the scanning step length, and reconstructs the measured surface height with high precision.
The detailed working principle of the scheme comprises the following steps:
step 1: acquiring interferograms in the vertical direction by using a white light interferometry device, wherein N pieces of interferograms are acquired, lambda is the equivalent wavelength of the white light interferometry device, sigma is the angular wave number corresponding to the equivalent wavelength lambda, and sigma is 2 pi/lambda;
step 2: respectively calculating the definition S of N interferograms by using a definition operatori(i-1, 2, …, N) or Si>(hs) marking the i-th frame interference icon as an effective interference image, wherein the ths is a preset threshold value;
and 3, step 3: arranging the effective interference patterns into an effective interference pattern sequence according to the sequence of the sequence numbers from small to large, and renumbering, wherein the effective interference patterns are marked as Ii(x, y), where the index i is 1,2, …, M is the number of effective interferograms, and (x, y) is the number of pixel points on an effective interferogram;
and 4, step 4: continuously sequencing the effective interference pattern sequence according to sequence numbers to divide the effective interference pattern sequence into P groups, wherein each group has Q interference patterns, R is the number of overlapped amplitudes in two adjacent groups, and R is more than 0 and less than Q;
and 5, step 5: calculating the gray scale change v of the pixel point (x, y) on the p-th group of effective interference image along the sequence number directionp(x,y)，vp(x,y)>thv, marking the pixel points as effective pixel points of the p-th group of effective interferograms to obtain all effective pixel points of the p-th group of effective interferograms, wherein thv is a preset threshold value;
and 6, step 6: calculating phase shift stepping values d of all effective pixel points on the p-th group of effective interferograms by adopting a phase shift calculation methodp,q，q＝2,3,…,Q；
And 7, step 7: repeating the 5 th step and the 6 th step, and calculating the phase shift stepping value d of the P groups of effective interferogramsp,q，p＝1,2,…,P，q＝2,3,…,Q；
And 8, step 8: averaging the phase shift stepping values of the adjacent groups of overlapped R effective interferograms, directly taking the phase shift stepping value obtained in the step 6 from the non-overlapped effective interferogram to obtain the phase shift stepping value of each interferogram in the effective interferogram sequence, and recording the phase shift stepping value as DjJ 2,3, …, M, and let Dj＝0；
Step 9: calculating the scanning height z of each interferogram in the effective interferogram sequence relative to the first interferogramj，j＝1,2,…,M，
Step 10: dividing the effective interferograms into G groups, wherein each group has T interferograms, two adjacent groups have T-1 interferograms which are overlapped, G is M- (T-1), the T-th interferogram in each group is defined as a characteristic interferogram of the group, and T is more than or equal to 1 and less than or equal to T;
and 11, step 11: calculating the modulation degree M of each pixel point (x, y) on the g-th group of characteristic interferogramsg(x, y) and phase
sk＝sin[2σ(zg+k-1-zg+t-1)]；
ck＝cos[2σ(zg+k-1-zg+t-1)]；；
Step 12: repeating the step 11 until the G groups of interferograms complete calculation, and obtaining R- (T-1) M pixels for each pixel point (x, y)g(x, y) and R- (T-1)
Step 13: for pixel point (x, y), find M in the direction of sequence numbergThe number S (x, y) with the largest numerical value (x, y);
step 14: calculating the height h (x, y) of the pixel point (x, y),
the phase shift calculation method can be a three-amplitude arcsine algorithm or an iterative algorithm.
The three arcsine algorithms comprise the following steps:
step 1: averaging the gray levels of each pixel point (x, y) of the effective interference image along the sequence number direction to obtain a background A (x, y) of the effective interference image;
step 2: subtracting A (x, y) from each effective interferogram to obtain a background-free interferogram Iq'(x,y)，q＝1,2,…,Q；
And 3, step 3: the phase shift step value of the q-th effective interferogram is
Q2, 3, …, Q, Pos is Iq'(x,y)>0, Neg is Iq'(x,y)<0, wherein the nominal scanning step length of the three arcsine algorithms is lambda/8.
The iterative algorithm comprises N loops, and each loop comprises a calculation part I and a calculation part II.
Said calculating part I knowing the time phase delta of the effective interferogramqQ is 1,2, …, Q, calculating the spatial phase of the effective pixel point
The calculation method is
Q is the number of interferograms involved in the calculation, δ for cycle 1qIs the initial value of the input, δ for the non-1 st cycleqObtained from the previous calculating part II;
the calculation part II is used for knowing the space phase of the effective pixel point
Calculating the time phase delta of the effective interferogramqThe calculation method is
PixNam is the number of effective pixel points participating in calculation, and the spatial phase
Obtained from the calculation part I;
the number N of the circulation is directly specified in advance, or delta calculated by comparing two adjacent circulation is comparedqDeviation, if the deviation is less than a pre-specified threshold, the loop terminates;
phase shift step value dq＝δq-δq-1，q＝2,3,…,Q。
Compared with the prior art, the invention has the following advantages and beneficial effects:
(1) the acquired interference fringes are analyzed without adding a detection light path and a related feedback control module, so that the complexity of the system, the volume of the instrument and the cost of the instrument can be reduced;
(2) when the scanning step length is calculated, the state of the scanning error is not limited, the scanning error can be accurately calculated, and the method is suitable for the conditions of low frequency, medium-high frequency and random scanning errors.
(3) And during surface reconstruction, the modulation degree and the phase are calculated according to the actual scanning step length, the scanning error compensation is carried out on the interference signal, and the precision of surface reconstruction is improved.
Drawings
FIG. 1 is a flow chart of a scanning error self-correcting white light interferometry method of the present invention.
FIG. 2 is an interferogram acquired according to an embodiment of the present invention.
FIG. 3 is a diagram of an effective pixel area corresponding to an interference pattern according to an embodiment of the present invention.
FIG. 4 is a flow chart of the three arcsine algorithm of the present invention.
Fig. 5 is a diagram of phase shift step values calculated using three arcsine algorithms in accordance with an embodiment of the present invention.
FIG. 6 is a flow chart of an iterative algorithm of the present invention.
Fig. 7 is a diagram of phase shift step values calculated using an iterative algorithm in accordance with an embodiment of the present invention.
FIG. 8 shows the modulation and phase of the pixels (100 ) calculated according to an embodiment of the present invention.
Fig. 9 is a reconstructed surface of a test object according to an embodiment of the present invention.
Detailed Description
The present invention will be described in further detail with reference to examples.
Example (b): as shown in fig. 1 to 9, this embodiment measures a step having a nominal height of 1.8 μm. The white light interferometry device has a magnification of 10, an equivalent wavelength λ of 0.6046 μm, and a preset scanning step of λ/8-75.6 nm. During the measurement process, the measurement device is disturbed by the vibration of unknown parameters. The example was carried out according to the scheme of FIG. 1. Scanning from the bottom to the top of the step was completed, and a total of N-261 interferograms were acquired, with an interferogram resolution of 616 × 514. Calculating the definition S of each interference pattern on the whole pattern by using the principle that the image gray scale is strongly changed due to the stripes and the normalized root mean square definition operatoriThe threshold ths is set to 0.02. Finally, there are 173 effective interferograms, of which the 83 th interferogram is shown in fig. 2. The interferogram collected in white light interferometry can be represented as:
since two phase shift calculation methods are involved, and the involved grouping and calculation methods are different, the process and principle of determining the phase shift stepping value by the two phase shift calculation methods are described below.
(a) Three-amplitude arcsine algorithm
Dividing the effective interferograms into 169 groups, wherein the quantity Q of each group of interferograms is 3, and the quantity R of the interferograms of the adjacent groups is 2. Then, for each group of interferograms, the gray scale variation of each pixel point along the sequence number direction is calculated, and the gray scale variation is expressed by a normalized root mean square value in the embodiment. The normalized root mean square value is the mean square root of the pixel gray level divided by the gray level. The threshold thv of this embodiment is 0.1. Taking the 82 nd set of interferograms as an example, effective pixel points of the 82 nd set of interferograms are calculated as shown in fig. 3. The present embodiment uses three-sine algorithms to calculate the phase shift step value according to the process shown in fig. 4. And (3) averaging along the sequence number direction to estimate the background A (x, y) of each pixel, and subtracting the obtained background A (x, y) from the formula (1) to obtain a background-free interferogram. The nominal value of the scanning step is lambda/8, corresponding to a phase shift step value of pi/2 between two steps. The conversion idea can regard the scanning error as the value of the actual scanning step length deviation pi/2 and record as epsilon. The envelope values of the interferograms are approximately the same within one interference period, and the background-free interferogram can be expressed as:
surface phase
π/2+ε＝2kΔjScanning step size Δj＝zj+1-zj＝zj-zj-1. Thus, the value of the deviation of π/2 of the jth interferogram can be calculated from equation (2):
in view of
Time, denominator Ij' (x, y) is approximately zero, the resulting error of ε is amplified, and therefore pixels of π/2 need to be avoided. Accordingly, according to l'jThe symbol of (x, y) divides all points in the active area into P, N sets, P is Ij'(x,y)>0, N is Ij'(x,y)<And all pixel points of 0 are collected. Synthesizing P, N pixel points to obtain
Thereby obtaining a phase shift step value of
In this embodiment, the number of effective interferogram overlaps is 2, and since the number of interferograms in each group is small (Q is 3), D is directly taken without averagingj＝dj. The present embodiment uses three arcsine algorithms to calculate the phase shift step values of the effective interferogram as shown in fig. 5.
(b) Iterative algorithm
Dividing the effective interferograms into 42 groups, wherein the quantity Q of each group of interferograms is 7, and the quantity R of the interferograms of the adjacent groups is 3. And determining effective pixel points of each group of interferograms according to the method of three arcsine algorithms, and calculating a phase shift stepping value according to the flow shown in fig. 6. Considering that the modulation degree is approximately constant for each set of interferograms, equation (1) can be simplified as:
spatial phase of effective pixel
Time phase delta of effective interferogramq＝2kzqWithin each group, z is defaulted10. Nominal value of the scanning step is lambda/8, the preset time phase deltaq(q-1) × 2 kxλ/8 ═ q-1) pi/2, as the time phase δ of the computation portion i in cycle 1q。
The calculation part I uses the least square method to calculate the time phase delta from the known timeqComputing spatial phase
The purpose of least squares is to find
Satisfy the requirement of
By function expansion and differentiation, the solution is obtained
The formula of (a):
the calculation part II uses the least square method to calculate the phase from the known space phase
Calculating the time phase deltaq. The purpose of the least squares is to find δqSatisfy the requirement of
Solving delta is obtained by function expansion and differentiationqThe formula of (a):
PixNam is the number of effective pixels participating in the calculation. In the present embodiment, for the interferogram shown in fig. 2, the number of effective pixels PixNum equals 57112 corresponding to the p-th 20 th group of interferograms.
In this embodiment, when the iterative algorithm is used to calculate the phase shift amount, the number of cycles N is set>The iteration automatically terminates at time 5. After the calculation is terminated, delta is obtainedqPerforming adjacent difference to obtain a phase shift step value deltaqI.e. dq＝δq-δq-1，q＝2,3,…,Q。
The present embodiment uses an iterative algorithm, each set yielding 6 phase shift step values (d)10, not counting inside),wherein d of each group2、d3D from the previous group6、d7Are overlapping, d of each group6、d7With d of the next group2、d3Are overlapping. In this embodiment, two phase shift step values overlapped between two groups are used for averaging, that is
To reduce the effect of errors. D for non-overlapping interferograms4、d5Taking D directly without averaging4＝d4、D5＝d5. The present embodiment uses an iterative algorithm to calculate the phase shift step values of the effective interferogram as shown in fig. 7.
The above is the calculation process of the three arcsine algorithms and the iterative algorithm in this embodiment. In order to avoid repetition, phase shift stepping values calculated by three arcsine algorithms are adopted as specific description objects in the steps (9 th to 14 th) after description.
And accumulating the obtained phase shift stepping values, and converting the phase shift stepping values into height values to obtain the scanning height of each interference pattern in the effective interference pattern sequence relative to the first interference pattern. When the modulation degree and the phase are calculated, the effective interferograms are divided into groups of G169 by 5 interferograms per group and 4 overlaps between two groups. The characteristic interferogram of the group is taken as the interferogram in the middle of each group, namely t is 3.
Since the scanning step (phase shift step value) deviates from the preset value and is not uniform, the modulation degree and the phase cannot be calculated by adopting the equal step method. Assuming that the modulation degree in each group is the same, the modulation degree and the phase of the characteristic interferogram in each group can be calculated by adopting a least square method. The core idea of the calculation is the same as that of the calculation part II in the iterative algorithm. In the present embodiment, taking the pixel points (100 ) on the interferogram as an example, the modulation degree and phase calculated are shown in fig. 8. The maximum modulation degree serial number S (100 ) of the pixel point (100 ) is 158, and the corresponding scanning height z15810.8187 μm, phase
The height of the pixel points (100 ) can be calculated as
The heights of all the pixel points are calculated, the surface of the measuring object can be reconstructed, and the leveled step is shown in fig. 9. The step height was calculated to be about 1.7673 μm. This height is very close to the measurement result (1.768. + -. 0.010) μm, and the relative deviation is only 0.04%.
From the calculated phase shift step values, the actual phase shift step values deviate overall by pi/2 due to scanner errors and vibration disturbances, and vibration causes phase shift step values to fluctuate locally at high frequencies. These all bring obvious errors to the traditional white light interferometry method, the step height obtained by the traditional method is 1.7382 μm, and the relative deviation reaches 1.68%.
The above-mentioned embodiments are intended to illustrate the objects, technical solutions and advantages of the present invention in further detail, and it should be understood that the above-mentioned embodiments are merely exemplary embodiments of the present invention, and are not intended to limit the scope of the present invention, and any modifications, equivalent substitutions, improvements and the like made within the spirit and principle of the present invention should be included in the scope of the present invention.
Claims (10)
1. A scanning error self-correcting white light interferometry method is characterized by comprising the following steps:
s1: collecting N interferograms along the vertical direction by using a white light interferometry device;
s2: respectively calculating the definition of the N interference patterns by using a definition operator, and marking the effective interference patterns according to the definition;
s3: arranging the obtained effective interferograms into an effective interferogram sequence according to the sequence of the collected sequence numbers from small to large, coding again, and continuously sequencing the effective interferogram sequence according to the sequence numbers to divide the effective interferogram sequence into P groups, wherein each group has Q interferograms;
s4: calculating the gray scale change of pixel points on each group of effective interference patterns along the sequence number direction, and marking effective pixel points;
s5: calculating phase shift stepping values of all effective pixel points on each group of effective interferograms by adopting a phase shift calculation method;
s6: calculating the scanning height of each interferogram in the effective interferogram sequence relative to the first interferogram according to the phase shift stepping value;
s7: dividing the effective interferograms into G groups, wherein each group has T interferograms, defining the T-th interferogram in each group as a characteristic interferogram of the group, and calculating the modulation degree and the phase of each pixel point on each characteristic interferogram;
s8: and searching the serial number with the maximum modulation degree value in the serial number direction, and calculating the height of the pixel point according to the modulation degree and the phase.
2. The scanning error self-correcting white light interferometry method according to claim 1, wherein the step S2 further comprises the following sub-steps: calculating the resolution as SiI ═ 1,2, …, N; if Si>And ths, recording the interference icon of the ith frame as an effective interference map, wherein the ths is a preset threshold value.
3. The white light interferometry method for self-correcting scanning errors according to claim 2, wherein the step S3 further comprises the following sub-steps: when renumbering, the effective interference pattern is marked as Ii(x, y), where the index i is 1,2, …, M is the number of effective interferograms, and (x, y) is the number of pixel points on an effective interferogram.
4. The white light interferometry method for self-correcting scanning errors according to claim 3, wherein the step S4 further comprises the following sub-steps: calculating the gray scale change v of the pixel point (x, y) on the effective interference image in each group along the sequence number directionp(x,y)，vp(x,y)>thv, the pixel points are marked as effective pixel points of the p-th group of effective interferograms to obtain all effective pixel points of the p-th group of effective interferograms, thv is presetThe threshold value of (2).
5. The scanning error self-correcting white light interferometry method according to claim 1, wherein the step S5 further comprises the following sub-steps: the calculated phase shift step value of the p-th group of the q-th interferograms is recorded as dp,qWherein P is 1,2, …, P, Q is 2,3, …, Q; averaging the phase shift step values of the adjacent groups of overlapped R effective interferograms, and directly taking the phase shift step value d obtained in the step S5 for the non-overlapped effective interferogramsp,qObtaining the phase shift stepping value of each interferogram in the effective interferogram sequence and recording the phase shift stepping value as DjJ is 2,3, …, M is the number of effective interferograms, and let D be1Where R is the number of overlapping amplitudes in two adjacent groups, 0<R<Q。
6. The white light interferometry method for self-correcting scanning errors according to claim 5, wherein the step S6 further comprises the following sub-steps: let the scan height be zjWhere j is 1,2, …, M, j is the interferogram number of the scanning height to be calculated, DiIs the phase shift step value of the ith interferogram, sigma is the angle wave number corresponding to the equivalent wavelength lambda, and sigma is 2 pi/lambda;
7. the scanning error self-correcting white light interferometry method according to claim 3, wherein the step S7 further comprises the following sub-steps: dividing the effective interferograms into G groups, wherein each group has T interferograms, two adjacent groups have T-1 interferograms which are overlapped, G is M- (T-1), the T-th interferogram in each group is defined as a characteristic interferogram of the group, and T is more than or equal to 1 and less than or equal to T; then, the modulation degree M of each pixel point (x, y) on the g group characteristic interference pattern is calculatedg(x, y) and phase
sk＝sin[2σ(zg+k-1-zg+t-1)]；
ck＝cos[2σ(zg+k-1-zg+t-1)]；
Until G groups of interferograms complete calculation, and for each pixel point (x, y), obtaining R- (T-1) Mg(x, y) and R- (T-1)
Where A is the background intensity, b is the modulation cosine component, c is the modulation sine component, SkIs the sine value of the phase shift of the g + k-1 th interferogram relative to the g + t-1 th interferogram, CkIs the cosine of the phase shift of the g + k-1 th interferogram relative to the g + t-1 th interferogram, σ is the angular wave number corresponding to the equivalent wavelength λ, and σ is 2 π/λ.
8. The white light interferometry method for self-correcting scanning errors according to claim 7, wherein the step S8 further comprises the following sub-steps: for pixel point (x, y), find M in the direction of sequence numbergThe number S (x, y) with the largest numerical value (x, y); calculating the height h (x, y) of the pixel point (x, y):
wherein ZS(x，y)Is the scanning height corresponding to the pixel (x, y) on the interference pattern with the sequence number S (x, y),
is the phase corresponding to the pixel (x, y) on the S (x, y) interferogram.
9. The white light interferometry method for self-correction of scanning errors according to claim 3, wherein said phase shift calculation method employs three arcsine algorithms, said three arcsine algorithms comprising the steps of:
s21: averaging the gray levels of each pixel point (x, y) of the effective interference image along the sequence number direction to obtain a background A (x, y) of the effective interference image;
s22: subtracting A (x, y) from each effective interferogram to obtain a background-free interferogram Iq'(x,y)，q＝1,2,…,Q；
S23: the phase shift step value of the q-th effective interferogram is
Q2, 3, …, Q, Pos is Iq'(x,y)>0, Neg is Iq'(x,y)<0, wherein the nominal scanning step length of the three arcsine algorithms is lambda/8.
10. The white light interferometry method for self-correcting scanning errors according to claim 3, wherein the phase shift calculation method adopts an iterative algorithm, the iterative algorithm comprises N cycles, and each cycle comprises a calculation part I and a calculation part II;
in said calculation part I, the time phase delta of the effective interferogram is knownqQ is 1,2, …, Q is the number of interferograms involved in the calculation of the spatial phase of the active pixel
The calculation method is
A is the background intensity, b is the modulation degree cosine component, c is the modulation degree sine component;
for cycle 1, δqIs the initial value of the input, δ for the non-1 st cycleqObtained from the calculation part II of the previous cycle;
the computing part II knows the space phase of the effective pixel point
Calculating the time phase delta of the effective interferogram of all Q interferogramsqQ is 1,2, …, Q, the calculation method is
PixNam is the number of effective pixel points participating in calculation, A ' is background intensity, b ' is modulation degree cosine component, and c ' is modulation degree sine component;
spatial phase
Obtained from the calculation part I of the cycle;
the number N of the cycles is directly specified in advance, or delta calculated by comparing two adjacent cyclesqDeviation is determined ifIf the deviation is less than a pre-specified threshold, the cycle is terminated;
phase shift step value dq＝δq-δq-1，q＝2,3,…,Q。
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